名校
解题方法
1 . 记等差数列
的前
项和为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554e6c461ccc5aa3093c524aa528a4e2.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ba58bbd886450561d3104017aada2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554e6c461ccc5aa3093c524aa528a4e2.png)
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名校
解题方法
2 . 数列
的最小项的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a172d5c20966486c73bc33817b3be8bc.png)
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名校
3 . 数列
满足
(
为正整数),且
与
的等差中项是5,则首项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ce9d5623b21817dd182b9058dc271a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
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昨日更新
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3卷引用:上海市格致中学2024届高三下学期三模数学试卷
4 . 若数列
是首项为1,公比为2的等比数列,记其前n项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
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真题
5 . 无穷等比数列
满足首项
,记
,若对任意正整数
集合
是闭区间,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b67857a043caf87b55d38401d0d9062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d59e4e49e9b0b2493f18b41e260da5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72f2cbabcb955a433e99bf0ee8ec020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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真题
6 . 已知
则不等式
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbce12f6911dacf78262ba950c0be55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e1bcced697608aa2a6c6afcc181da7.png)
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名校
解题方法
7 . 已知无穷数列
的前
项和为
,不等式
对任意不等于2的正整数
恒成立,且
,那么这样的数列有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d896cc62945587c910c3ea157d1bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80759fdc78c76b05dab66c325f48a443.png)
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名校
8 . 设关于x的方程
的从小到大的第i个非负解为
,若数列
是无穷等差数列,且
在区间
中的项恰好比在区间
中的项少2项,则ω的取值集合为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4aef8fc10674359b41c70424c7b696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45016247370f5b00aeb0882977abb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583dfca240679328ffcbbe457ec5bdd8.png)
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名校
9 . 早在西元前6世纪,毕达哥拉斯学派已经知道算术中项,几何中项以及调和中项,毕达哥拉斯学派哲学家阿契塔在《论音乐》中定义了上述三类中项,其中算术中项,几何中项的定义与今天大致相同.若
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0a41e2a5aaf613e467c55837183e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c2c9c964455e60490cbed197380fc4.png)
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名校
10 . 设
是等比数列
的前
项和,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130aab74cff7810ad14ac2480ff5b929.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c705ed1d40eb3d40ebadd05dbb645b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc737fd79335e429f265108d8dd2504c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130aab74cff7810ad14ac2480ff5b929.png)
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